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Basic Information

Early Soviet lunar exploration satellites' series had their development designations beginning with E. Thus, E-1 was direct hit on the lunar surface (Luna_1 and Luna_2); E-2 was lunar fly-by probe which should made photos of far side of the Moon (Luna_3), E-5 was inteded to acquire the high-resolution photos of the Luna; E-5 involved soft-landing and getting panoramic view of lunar surface (it took Luna_5 to Luna_9 launces to be actually achieved).

Programma E-3 (brainchild of Academician Zeldovich) stood aside of these as most exotic. This one should provide the undeinable proof thet Soviet Union had reached the Moon. It should be as influental as Sputnik, which was witnessed by everybody.

E-3 satellites were ones with nuclear charges delivered and detonated at Moon surface. Resulting flash should be (according to initial estimations) visible on Earth with the simplest of optical equipment.
Development of this research project continued for some time: the dummy of nuclear charge was made and prepared for testing.

Head rocket scientists of Soviet Union were opposed of the proposition: they were too aware of possible consequences of failure of carrier missile. Failure of first stage engines meant that nuclear charge detonates on the territory of USSR; second and third stage failure ment that the satellite lands outside of Soviet Union (perhaps on the territory of other sovereign state). Failure of third stage may strand it on low-Earth orbit, and mid-course correction going wrong might send it in the trip around Sun — it would be navigation hazard for the spaceships to come.
Another line of opposition came from politicians — if USSR warns the world about the launch, it'd cause an uproar: derisive if they fail, angry if they succed and hostile in both cases.
Nuclear physicist doubted that in the absence of athmospere the small nuclear charge could produce a large enough flash.
As a result of these arguments, the existence of E-3 was never reported to Nikita Khruschev.

Finally, Programma E-3 was buried. It has to be noted that Yakov Zeldovich was the first to denounce the idea.

Sources

Game and Story Use

Given more adventurous scientists (ones having '30s mentality with posession of '50s technology), E-3 might came true…

…which could trigger the World War III (or even World War II).

…or might be constant headache of spacefarers of future.

Note that Programma E-4 is missing in the descriptions above. It is explained as bureaucratic mishap, but what if it was even more exotic than E-3?